Generalized neck analysis of harmonic maps from surfaces

TL;DR

This paper investigates the behavior of harmonic maps from surfaces with bounded energy, focusing on the generalized neck domain, and analyzes the limits of nullity and index in the sequence.

Contribution

It introduces a new analysis of harmonic maps on generalized neck domains, providing bounds on energy density and insights into nullity and index limits.

Findings

Upper bound of energy density established

Limit behavior of nullity analyzed

Limit behavior of index analyzed

Abstract

In this paper, we study the behavior of a sequence of harmonic maps from surfaces with uniformly bounded energy on the generalized neck domain. The generalized neck domain is a union of ghost bubbles and annular neck domains, which connects non-trivial bubbles. An upper bound of the energy density is proved and we use it to study the limit of the nullity and index of the sequence.